Totally 100% with this. When younger I thought I could read the material and say "Oh, okay that makes sense I understand this." Only to fail miserably when on a test or somewhere I had to apply what I "knew" and realizing I didn't actually know it. I lean strongly toward autodidacticism and learned that if I could solve problems with the technique then I knew it.
My calculus 1 professor gave the advice that the best way to study is to do every problem in the book, then go and get another book and do every problem in that book, and keep doing that until you look at a problem and know exactly every step to do immediately.
There’s certainly fields of math where I’ve seen a twist on the advice. Differential geometry, for example, is a big field with a lot of notation. Different textbooks end up using very different notations and covering non-overlapping sections of the field. Therefore, the advice I got was to not just do the problems, but translate the definitions and theorems into a unified notation that you feel is natural.
That's how I learned probability theory. I studied from one book and solved all problems, then moved to the next, until it became second nature. Probability theory is one of the topics that you will never learn by only reading, it is necessary to develop the necessary intuition.
Which exactly describes the problem with today's culture of people watching a 10 minute youtube clip and then thinking they are experts on the subject matter.
